ALEX Lesson Plans
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Title: Nets: Message in a Box
Description:
In cooperative/collaborative groups, students will compare and contrast a twodimensional pattern and a threedimensional shape. Students will use a net to label and then construct a rectangular prism. Students will find the surface area of a rectangular prism. As a final performance task, students will create a message box.
Standard(s): [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4]
Subject: Mathematics (6)
Title: Nets: Message in a Box
Description: In cooperative/collaborative groups, students will compare and contrast a twodimensional pattern and a threedimensional shape. Students will use a net to label and then construct a rectangular prism. Students will find the surface area of a rectangular prism. As a final performance task, students will create a message box.
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Title: Grow a GEM
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Students will grow crystals out of different substances. Students will also document and make a podcast video of the growth of their crystals. Students will make and identify different geometric shapes.
This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (5) 25: Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. [5G3] [S1] (5) 10: Identify spheres of Earth, including the geosphere, atmosphere, and hydrosphere. [S1] (6) 4: Explain the plate tectonic theory.
Subject: Mathematics (5  6), or Science (5  6)
Title: Grow a GEM
Description: Students will grow crystals out of different substances. Students will also document and make a podcast video of the growth of their crystals. Students will make and identify different geometric shapes.
This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Painting the Pyramids
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The students will find the area of each two dimensional figure on a net of a square pyramid. In groups, students will cut out the net and create a square pyramid. Groups will then discuss how to find the lateral area and the total surface area of the solid.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
Standard(s): [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (7) 13: Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. [7G3] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
Subject: Mathematics (6  7)
Title: Painting the Pyramids
Description: The students will find the area of each two dimensional figure on a net of a square pyramid. In groups, students will cut out the net and create a square pyramid. Groups will then discuss how to find the lateral area and the total surface area of the solid.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
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Title: Cutting the CHEESE
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The students will find the area of each two dimensional figure on a net of a triangular prism. In groups, students will cut out the net and create a triangular prism. Groups will then discuss how to find the lateral area and the total surface area of the solid.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
Standard(s): [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
Subject: Mathematics (6  7)
Title: Cutting the CHEESE
Description: The students will find the area of each two dimensional figure on a net of a triangular prism. In groups, students will cut out the net and create a triangular prism. Groups will then discuss how to find the lateral area and the total surface area of the solid.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
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Title: Nifty Nets
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During this activity, students will create nets for prisms. They will find the volume and surface area of the shapes. They will also use interactive activities to review threedimensional shapes.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Standard(s): [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve realworld and mathematical problems. [8G9]
Subject: Mathematics (6  8)
Title: Nifty Nets
Description: During this activity, students will create nets for prisms. They will find the volume and surface area of the shapes. They will also use interactive activities to review threedimensional shapes.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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Title: "Movin' On Up"
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Students will use their knowledge of scale factor to enlarge a picture to scale. They will then use PhotoStory to create a collage of their pictures.
This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Standard(s): [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (7) 11: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. [7G1]
Subject: Mathematics (6  7)
Title: "Movin' On Up"
Description: Students will use their knowledge of scale factor to enlarge a picture to scale. They will then use PhotoStory to create a collage of their pictures.
This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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Title: Thinking outside the "BOX"
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The students will find the area of each two dimensional figure on a net of a rectangular prism. In groups, students will cut out the net and create a rectangular prism. Groups will then discuss how to find the lateral area and the total surface area of the solid.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
Standard(s): [MA2013] (6) 21: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. [6G1] [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
Subject: Mathematics (6  7)
Title: Thinking outside the "BOX"
Description: The students will find the area of each two dimensional figure on a net of a rectangular prism. In groups, students will cut out the net and create a rectangular prism. Groups will then discuss how to find the lateral area and the total surface area of the solid.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
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Title: Ping Pong Madness
Description:
In this lesson, students will use their knowledge of 3D shapes to create packages for ping pong balls. They must create small, medium and large packages that are cost effective and stack easily. They will make nets of the their packages and find the volume and surface area of each. Students will present the information using a multimedia presentation and a spreadsheet software. This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Standard(s): [TC2] (68) 2: Publish digital products that communicate curriculum concepts. [MA2013] (5) 20: Recognize volume as an attribute of solid figures, and understand concepts of volume measurement. [5MD3] [MA2013] (5) 21: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. [5MD4] [MA2013] (5) 22: Relate volume to the operations of multiplication and addition, and solve realworld and mathematical problems involving volume. [5MD5] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4]
Subject: Mathematics (5  7), or Technology Education (6  8)
Title: Ping Pong Madness
Description: In this lesson, students will use their knowledge of 3D shapes to create packages for ping pong balls. They must create small, medium and large packages that are cost effective and stack easily. They will make nets of the their packages and find the volume and surface area of each. Students will present the information using a multimedia presentation and a spreadsheet software. This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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Title: Golden Ratios of the Body, Architecture, and Nature
Description:
Students will study the golden ratio as it relates to human body measurements, architecture, and nature. Students will use a desktop publishing program to create a poster. The poster will have digital photos of themselves, architecture samples, or nature examples. Students will also include a spreadsheet with the lengths, widths, and length/width ratios of the samples included in the photos.
Standard(s): [TC2] CA2 (912) 5: Utilize advanced features of spreadsheet software, including creating charts and graphs,
sorting and filtering data, creating formulas, and applying functions. [MA2013] MI1 (912) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama) [MA2013] MI1 (912) 3: Use special numbers, including e, i, π and the golden ratio, to solve applicationbased problems. [MA2013] GEO (912) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [GMG3] [MA2013] ALC (912) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama) [MA2013] ALC (912) 9: Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. (Alabama) [MA2013] (7) 20: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. [7SP4] [MA2013] (7) 11: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. [7G1] [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [MA2013] (7) 1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. [7RP1] [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4]
Subject: Mathematics (6  12), or Technology Education (9  12)
Title: Golden Ratios of the Body, Architecture, and Nature
Description: Students will study the golden ratio as it relates to human body measurements, architecture, and nature. Students will use a desktop publishing program to create a poster. The poster will have digital photos of themselves, architecture samples, or nature examples. Students will also include a spreadsheet with the lengths, widths, and length/width ratios of the samples included in the photos.
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Title: Cubes Everywhere
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In this Illuminations lesson, students use cubes to develop spatial thinking and review basic geometric principles through reallife applications. Students are given the opportunity to build and take apart structures based on cubes.
Standard(s): [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (7) 11: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. [7G1] [MA2013] (7) 12: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. [7G2] [MA2013] (7) 13: Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. [7G3] [MA2013] GEO (912) 38: Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. [GGMD4] [MA2013] GEO (912) 39: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [GMG1] [MA2013] GEO (912) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [GMG3]
Subject: Mathematics Title: Cubes Everywhere
Description: In this Illuminations lesson, students use cubes to develop spatial thinking and review basic geometric principles through reallife applications. Students are given the opportunity to build and take apart structures based on cubes. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Are They Possible?
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In this lesson, one of a multipart unit from Illuminations, students examine some isometric drawings that seem to be impossible. They investigate one method that Dutch artist M.C. Escher used to create such impossible figures.
Standard(s): [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4]
Subject: Mathematics Title: Are They Possible?
Description: In this lesson, one of a multipart unit from Illuminations, students examine some isometric drawings that seem to be impossible. They investigate one method that Dutch artist M.C. Escher used to create such impossible figures. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Are They Possible? Overhead
Description:
This reproducible transparency, from an Illuminations lesson, depicts several isometric drawings of several '' impossible'' figures.
Standard(s): [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] GEO (912) 36: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [GGMD3] [MA2013] GEO (912) 37: Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama)
Subject: Mathematics Title: Are They Possible? Overhead
Description: This reproducible transparency, from an Illuminations lesson, depicts several isometric drawings of several '' impossible'' figures. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Building Using the FrontRightTop View
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In this lesson, one of a multipart unit from Illuminations, students explore drawing the frontrighttop view when given a three dimensional figure built from cubes. Students also explore building a three dimensional figure when given the frontrighttop view.
Standard(s): [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (7) 13: Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. [7G3] [MA2013] (8) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve realworld and mathematical problems. [8G9] [MA2013] GEO (912) 36: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [GGMD3] [MA2013] GEO (912) 38: Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. [GGMD4]
Subject: Mathematics Title: Building Using the FrontRightTop View
Description: In this lesson, one of a multipart unit from Illuminations, students explore drawing the frontrighttop view when given a three dimensional figure built from cubes. Students also explore building a three dimensional figure when given the frontrighttop view. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Do They Match? Overhead
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This reproducible transparency, from an Illuminations lesson, depicts several pairs of isometric drawings of threedimensional figures. Students determine whether the drawings in each pair represent the same shape as one another.
Standard(s): [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] GEO (912) 36: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [GGMD3]
Subject: Mathematics Title: Do They Match? Overhead
Description: This reproducible transparency, from an Illuminations lesson, depicts several pairs of isometric drawings of threedimensional figures. Students determine whether the drawings in each pair represent the same shape as one another. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Do They Match?
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In this lesson, one of a multipart unit from Illuminations, students use three dimensional figures they have constructed to determine when two isometric drawings can represent the same shape. They also determine what possible shapes might have the same isometric drawing and explain their reasoning.
Standard(s): [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (7) 13: Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. [7G3] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
Subject: Mathematics Title: Do They Match?
Description: In this lesson, one of a multipart unit from Illuminations, students use three dimensional figures they have constructed to determine when two isometric drawings can represent the same shape. They also determine what possible shapes might have the same isometric drawing and explain their reasoning. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Exploring the Isometric Drawing Tool
Description:
In this lesson, one of a multipart unit from Illuminations, students explore using an isometric drawing tool and gain practice and experience in manipulating drawings. They explore polyhedra using different representations and perspectives.
Standard(s): [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (7) 12: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. [7G2] [MA2013] (7) 13: Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. [7G3] [MA2013] (8) 16: Verify experimentally the properties of rotations, reflections, and translations: [8G1] [MA2013] (8) 17: Understand that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. [8G2] [MA2013] (8) 19: Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them. [8G4] [MA2013] GEO (912) 2: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). [GCO2] [MA2013] GEO (912) 5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. [GCO5] [MA2013] GEO (912) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [GCO12] [MA2013] GEO (912) 38: Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. [GGMD4]
Subject: Mathematics Title: Exploring the Isometric Drawing Tool
Description: In this lesson, one of a multipart unit from Illuminations, students explore using an isometric drawing tool and gain practice and experience in manipulating drawings. They explore polyhedra using different representations and perspectives. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Frontrighttop Views
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This reproducible transparency, from an Illuminations lesson, depicts an isometric drawing of a threedimensional figure, along with its front, right, and top views.
Standard(s): [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
Subject: Mathematics Title: Frontrighttop Views
Description: This reproducible transparency, from an Illuminations lesson, depicts an isometric drawing of a threedimensional figure, along with its front, right, and top views. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Mat Plans
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In this lesson, one of a multipart unit from Illuminations, students explore drawing a mat plan when given a three dimensional figure built from cubes. Students also explore building a three dimensional figure when given the mat plan.
Standard(s): [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (7) 13: Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. [7G3]
Subject: Mathematics Title: Mat Plans
Description: In this lesson, one of a multipart unit from Illuminations, students explore drawing a mat plan when given a three dimensional figure built from cubes. Students also explore building a three dimensional figure when given the mat plan. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Mat Plans: Overhead
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This reproducible transparency, from an Illuminations lesson, depicts an isometric drawing of a threedimensional figure along with its mat plan.
Standard(s): [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (7) 13: Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. [7G3]
Subject: Mathematics Title: Mat Plans: Overhead
Description: This reproducible transparency, from an Illuminations lesson, depicts an isometric drawing of a threedimensional figure along with its mat plan. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Using Cubes and Isometric Drawings
Description:
In this unit of six lessons, from Illuminations, students explore polyhedra using different representations and perspectives for three dimensional block figures. In addition, students examine area and volume concepts for block figures within this context.
Standard(s): [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (7) 13: Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. [7G3] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] GEO (912) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [GCO12] [MA2013] GEO (912) 37: Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama) [MA2013] GEO (912) 38: Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. [GGMD4]
Subject: Mathematics Title: Using Cubes and Isometric Drawings
Description: In this unit of six lessons, from Illuminations, students explore polyhedra using different representations and perspectives for three dimensional block figures. In addition, students examine area and volume concepts for block figures within this context. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Go the Distance
Description:
This lesson is the fourth part of a fourpart Illuminations unit titled '' Analyzing Numeric and Geometric Patterns of Paper Pool.'' The interactive paper pool game in this unit provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple. At the end of the lesson, students write reports on their findings. This resource is referenced in the Illuminations unit titled '' Analyzing Numeric and Geometric Patterns of Paper Pool'' and is related to the Illuminations lessons titled '' Paper Pool Game,'' '' Explore More Tables,'' '' Look for Patterns.''
Standard(s): [MA2013] (6) 21: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. [6G1] [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (8) 16: Verify experimentally the properties of rotations, reflections, and translations: [8G1] [MA2013] (8) 17: Understand that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. [8G2] [MA2013] (8) 18: Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates. [8G3]
Subject: Language Arts,Mathematics Title: Go the Distance
Description: This lesson is the fourth part of a fourpart Illuminations unit titled '' Analyzing Numeric and Geometric Patterns of Paper Pool.'' The interactive paper pool game in this unit provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple. At the end of the lesson, students write reports on their findings. This resource is referenced in the Illuminations unit titled '' Analyzing Numeric and Geometric Patterns of Paper Pool'' and is related to the Illuminations lessons titled '' Paper Pool Game,'' '' Explore More Tables,'' '' Look for Patterns.'' Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Surface Area
Description:
This reproducible transparency, from an Illuminations lesson, features equations for finding the ratios for computing the surface area of cylinders and rectangular prisms.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (8) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve realworld and mathematical problems. [8G9]
Subject: Mathematics Title: Surface Area
Description: This reproducible transparency, from an Illuminations lesson, features equations for finding the ratios for computing the surface area of cylinders and rectangular prisms. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: How Solid are Your Skills with Geometry?
Digital Tool:
Geometric Solids Tool Web Address URL:
http://illuminations.nctm.org/ActivityDetail.aspx?ID=70 Standard(s):
[MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] Digital Tool Description: The Illuminations tool called Geometric Solids is an excellent way to enhance a lesson and provide students with a deeper understanding of the properties of geometric properties. This tool will help students learn the relationships between vertices, faces, and edges. This tool can help students master finding the surface area of threedimensional figures. This tool also demonstrates the relationship between the solid shapes and their nets, which is a skill that needs to be mastered for the ARMT.
Title: How Solid are Your Skills with Geometry? Digital Tool: Geometric Solids Tool Digital Tool Description: The Illuminations tool called Geometric Solids is an excellent way to enhance a lesson and provide students with a deeper understanding of the properties of geometric properties. This tool will help students learn the relationships between vertices, faces, and edges. This tool can help students master finding the surface area of threedimensional figures. This tool also demonstrates the relationship between the solid shapes and their nets, which is a skill that needs to be mastered for the ARMT.
ALEX Podcasts
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Title: Pi  The Mathematical Dessert
Overview:
Watch this podcast and discover the mathematical number pi! Discussion includes the history of pi, mathematical concept of pi, and modern notation of the ∏ symbol used today. Interesting trivia, jokes, pi reciting contests, and pi day celebrations are included. This podcast is a must to add to your mathematics classroom and especially any pi day celebration. Standard(s):
[MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] GEO (912) 36: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [GGMD3]
Pi  The Mathematical Dessert Overview: Watch this podcast and discover the mathematical number pi! Discussion includes the history of pi, mathematical concept of pi, and modern notation of the ∏ symbol used today. Interesting trivia, jokes, pi reciting contests, and pi day celebrations are included. This podcast is a must to add to your mathematics classroom and especially any pi day celebration.
Web Resources
Lesson Plans
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Title: Building a Box
Description:
This lesson uses a realworld situation to help develop students' spatial visualization skills and geometric understanding.
Standard(s): [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4]
Building a Box
http://illuminations...
This lesson uses a realworld situation to help develop students' spatial visualization skills and geometric understanding.
Interactives/Games
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Title: Gee Geometric
Description:
This is a geometric game for students to count faces, sides, and edges of solids.
Standard(s): [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4]
Gee Geometric
http://illuminations...
This is a geometric game for students to count faces, sides, and edges of solids.
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Title: Math Makes a Connection: Isometric and 3D Drawing Tool
Description:
On this interactive website, students may draw buildings using cubes. Students may peel away the layers and take different isometric views of the inside of the drawings.
Standard(s): [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4]
Math Makes a Connection: Isometric and 3D Drawing Tool
http://connectedmath...
On this interactive website, students may draw buildings using cubes. Students may peel away the layers and take different isometric views of the inside of the drawings.
Thinkfinity Learning Activities
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Title: Isometric Dot Paper
Description:
Print this isometric grid worksheet and use it to easily draw threedimensional figures, such as cubes.
Standard(s): [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (7) 12: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. [7G2] [MA2013] (7) 13: Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. [7G3]
Subject: Mathematics Title: Isometric Dot Paper
Description: Print this isometric grid worksheet and use it to easily draw threedimensional figures, such as cubes. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Isometric Drawing Tool
Description:
Create dynamic drawings on isometric dot paper with this interactive tool. Draw 2D and 3D figures using edges, faces, or cubes that you can shift, rotate, color, or decompose.
Standard(s): [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (3) 25: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. [3G2] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2] [MA2013] (5) 25: Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. [5G3] [MA2013] (5) 26: Classify twodimensional figures in a hierarchy based on properties. [5G4] [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (7) 12: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. [7G2] [MA2013] (7) 13: Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. [7G3] [MA2013] (8) 19: Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them. [8G4] [MA2013] GEO (912) 2: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). [GCO2] [MA2013] GEO (912) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [GCO12] [MA2013] GEO (912) 38: Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. [GGMD4]
Subject: Mathematics Title: Isometric Drawing Tool
Description: Create dynamic drawings on isometric dot paper with this interactive tool. Draw 2D and 3D figures using edges, faces, or cubes that you can shift, rotate, color, or decompose. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8,9,10,11,12
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Title: Dynamic Paper Tool
Description:
Create customized activity sheets for your classroom! Nets of 3D shapes, tessellations, coordinate graphs, and more  all based on your input.
Standard(s): [MA2013] (0) 17: Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. [KG1] [MA2013] (0) 18: Correctly name shapes regardless of their orientations or overall size. [KG2] [MA2013] (0) 19: Identify shapes as twodimensional (lying in a plane, "flat") or threedimensional ("solid"). [KG3] [MA2013] (0) 20: Analyze and compare two and threedimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices or "corners"), and other attributes (e.g., having sides of equal length). [KG4] [MA2013] (0) 21: Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. [KG5] [MA2013] (0) 22: Compose simple shapes to form larger shapes. [KG6] [MA2013] (6) 3: Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. [6RP3] [MA2013] (6) 9: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. [6NS6] [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4]
Subject: Mathematics Title: Dynamic Paper Tool
Description: Create customized activity sheets for your classroom! Nets of 3D shapes, tessellations, coordinate graphs, and more  all based on your input. Thinkfinity Partner: Illuminations Grade Span: K,1,2,3,4,5,6,7,8,9,10,11,12

